Online research in philosophy

The partial cooperation displayed by subjects in the Centipede Game deviates radically from the predictions of traditional game theory. Even standard, infinite population, evolutionary settings have failed to provide an explanation for this behavior. However, recent work in finite population evolutionary models has shown that such settings can produce radically different results from the standard models. This paper examines the evolution of partial cooperation in finite populations. The results reveal a new possible explanation that is not open to the standard models and gives us reason to be cautious when employing these otherwise helpful idealizations. *Received January 2007; revised November 2007. †To contact the author, please write to: Department of Logic and Philosophy of Science, University of California, 3151 Social Science Plaza A, Irvine, CA 92697-5100; e-mail: rsmead@uci.edu.

Ernst Mayr has criticised the methodology of population genetics for being essentialist: interested only in “types” as opposed to individuals. In fact, he goes so far as to claim that “he who does not understand the uniqueness of individuals is unable to understand the working of natural selection” (1982, 47). This is a strong claim indeed especially since many responsible for the development of population genetics (especially Fisher, Haldane, and Wright) were avid Darwinians. In order to unravel this apparent incompatibility I want to examine the possible sources and implications of essentialism in this context and show why the kind of mathematical analysis found in Fisher's work is better seen as responsible for extending the theory of natural selection to a broader context rather than inhibiting its applicability.

This paper addresses the question, which sex ratio will evolve in a population that is subject to mutation and drift. The problem is analyzed using a simulation model as well as analytical methods. A detailed simulation model for the evolution of a population's allele distribution shows that for the sex ratio game a wide spectrum of different population states may evolve from on the one hand a monomorphic state with one predominant allele and with all other alleles suppressed by the forces of selection, to on the other hand a polymorphism determined by recurrent mutations. Which of these states will evolve depends on the population size, the mating system and the rate of mutations. For the sex ratio game the evolutionarily stable strategy (ESS), as defined by evolutionary game theory, can only predict the population sex ratio but not the underlying stable population state. A comparison of different approaches to the problem shows that false predictions of the stable population states might result from two simplifying assumptions that are fairly common in evolutionary biology:a) it is assumed that mutations are rare events and there is never more than one mutant gene present in a population at any one time; b) a deterministic relationship is assumed between the fitness assigned to an individual's strategy and the individual's contribution to the gene pool of future generations.

Explaining the persistence of populations is an important quest in ecology, and is a modern manifestation of the balance of nature metaphor. Increasingly, however, ecologists see populations (and ecological systems generally) as not being in equilibrium or balance. The portrayal of ecological systems as “non-equilibrium” is seen as a strong alternative to deterministic or equilibrium ecology, but this approach fails to provide much theoretical or practical guidance, and warrants formalisation at a more fundamental level. This is available in adaptation theory, which allows population persistence to be explained as an epiphenomenon stemming from the maintenance, survival, movement and reproduction of individual organisms. These processes take place within a physicochemical and biotic environment that persists through structured annual cycles, but which is also spatiotemporally dynamic and subject to stochastic variation. The focus is thus shifted from the overproduction of offspring and the consequent density dependent population pressure thought to follow, to the adaptations and ecological circumstances that support those relatively few individuals that do survive.

Biologists studying ecology and evolution use the term “population” in many different ways. Yet little philosophical analysis of the concept has been done, either by biologists or philosophers, in contrast to the voluminous literature on the concept of “species.” This is in spite of the fact that “population” is arguably a far more central concept in ecological and evolutionary studies than “species” is. The fact that such a central concept has been employed in so many different ways is potentially problematic for the reason that inconsistent usages (especially when the usage has not been made explicit) might lead to false controversies in which disputants are simply talking past one another. However, the inconsistent usages are not the only, or even the most important reason to examine the concept. If any set of organisms is legitimately called a “population,” selection and drift processes become purely arbitrary, too. Moreover, key ecological variables, such as abundance and distribution, depend on a nonarbitrary way of identifying populations. I sketch the beginnings of a population concept, drawing inspiration from the Ghiselin-Hull individuality thesis, and show why some alternative approaches are nonstarters.

Population genetics attempts to measure the influence of the causes of evolution, viz., mutation, migration, natural selection, and random genetic drift, by understanding the way those causes change the genetics of populations. But how does it accomplish this goal? After a short introduction, we begin in section (2) with a brief historical outline of the origins of population genetics. In section (3), we sketch the model theoretic structure of population genetics, providing the flavor of the ways in which population genetics theory might be understood as incorporating causes. In sections (4) and (5) we discuss two specific problems concerning the relationship between population genetics and evolutionary causes, viz., the problem of conceptually distinguishing natural selection from random genetic drift, and the problem of interpreting fitness. In section (6), we briefly discuss the methodology and key epistemological problems faced by population geneticists in uncovering the causes of evolution. Section (7) of the essay contains concluding remarks.

A basic model of hierarchical structure, expressed by simple, linear differential equations, shows that the pattern of population growth is essentially determined by conditions of redundancy in the sub-structure of individuals. There does not exist any possible combination between growth rate and accident rate that could balance population numbers and/or the level of redundancy within the population; all possible combinations either lead to extinction or to positive population growth with a decline of the fraction of individuals with redundant substructure. Declining populations, however, can be held fluctuating between certain limits by periodic phases of sub-unit repair. These results are particularly pertinent to the population dynamics of diploid (polyploid) organisms.

Why do societies collapse? We use an individual-based evolutionary model to show that, in environmental conditions dominated by low-frequency variation (“red noise”), extirpation may be an outcome of the evolution of cultural capacity. Previous analytical models predicted an equilibrium between individual learners and social learners, or a contingent strategy in which individuals learn socially or individually depending on the circumstances. However, in red noise environments, whose main signature is that variation is concentrated in relatively large, relatively rare excursions, individual learning may be selected from the population. If the social learning system comes to lack sufficient individual learning or cognitively costly adaptive biases, behavior ceases tracking environmental variation. Then, when the environment does change, fitness declines and the population may collapse or even be extirpated. The modeled scenario broadly fits some human population collapses and might also explain nonhuman extirpations. Varying model parameters showed that the fixation of social learning is less likely when individual learning is less costly, when the environment is less red or more variable, with larger population sizes, and when learning is not conformist or is from parents rather than from the general population. Once social learning is fixed, extirpation is likely except when social learning is biased towards successful models. Thus, the risk of population collapse may be reduced by promoting individual learning and innovation over cultural conformity, or by preferential selection of relatively fit individuals as models for social learning. © 2009 Elsevier Inc. All rights reserved.

Two populations are subdivided into two categories of individuals (hawks and doves). Individuals fight to have access to a resource which is necessary for their survival. Conflicts occur between individuals belonging to the same population and to different populations. We investigate the long term effects of the conflicts on the stability of the community. The modelis a set of ODE's with four variables corresponding to hawk and dove individuals of the two populations. Two time scales are considered. A fast time scale is used to describe frequent encounters and fightings between individuals trying to monopolize the resource. A slow time scale is used for the demography and the long term effects of encounters. We use aggregation methods in order to reduce this model into a system of two ODE's only for the total densities of the two populations which is found to be a classical Lotka-Volterra competition model. We study different cases of proportions of hawks and doves in both populations on the global coexistence and the mutal exclusion of the two populations. Pure dove tactics in both populations are unstable. In cases of mixed hawk and dove in both populations, there is coexistence. Pure dove or mixed hawk-dove tactics in one population can coexist with pure hawks in the other one when the costs of fightings between hawks are large enough.

A wide range of ecological and evolutionary models predict variety in phenotype or behavior when a population is at equilibrium. This heterogeneity can be realized in different ways. For example, it can be realized through a complex population of individuals exhibiting different simple behaviors, or through a simple population of individuals exhibiting complex, varying behaviors. In some theoretical frameworks these different realizations are treated as equivalent, but natural selection distinguishes between these two alternatives in subtle ways. By investigating an increasingly complex series of models, from a simple fluctuating selection model up to a finite population hawk/dove game, we explore the selective pressures which discriminate between pure strategists, mixed at the population level, and individual mixed strategists. Our analysis reveals some important limitations to the “ESS” framework often employed to investigate the evolution of complex behavior.